1. Field of the Invention
The present invention relates to accelerometers of the type that include a micromechanical pendulum. More particularly, the invention pertains to such an accelerometer with control loop resetting.
2. Description of the Prior Art
Accelerometers that include a micromechanical pendulum in a differential capacitor arrangement with a resetting control loop are incorporated into, and proposed for, various basic devices. The operation of such an arrangement will be described with reference to the embodiments illustrated in FIGS. 2 and 3.
The first solution, shown in FIG. 2, employs a digital computer coupled to an analog charge amplifier. A computer 2 directs voltage pulses U1, U2 (see FIG. 4) alternately to an upper electrode E1 and to a lower electrode E2 arranged relative to a pendulum P. If the arrangement is mistuned, a charge difference flows via the pendulum P, which is amplified at U3 and is digitized at the A/D converter 4. The computer 2 linearizes the pendulum characteristics and compensates (as can be seen from the central and right-hand diagrams of FIG. 4) for accelerations acting on the pendulum P by the pulse-width ratios of the time-sequential voltage pulses U1 and U2, on the upper and lower electrodes E1, E2, respectively. At the same time, the computer 2 adjusts the offset of the pendulum P, and compensates for bias and scale factor, particularly as a function of temperature.
The second solution, illustrated in FIG. 3 and the three timing diagrams of FIG. 5, uses analog charge control with a digital section 1 for pulse-width resetting when the pendulum P is deflected. The individual charges on the two capacitors C1, C2 are defined by a precision current source 5 over a constant, short time interval (e.g. 25 xcexcs). In this case, only the current flowing via the pendulum P is controlled. Although the current is applied via the electrodes E1, E2, it is not governed by the control system 6, 7. The charge control means that the effective resetting force per electrode is independent of pendulum position and need not be linearized. The voltages on the electrodes E1, E2 will differ, however, when the pendulum P is deflected. The charge difference represents the pick off voltage located at the input of an operational amplifier 6. Acceleration is indicated by the charge difference, and is compensated by the pulse-width ratio. This is accomplished with a digital test within a separate time slot of, for example, 75 xcexcs.
The two known solutions explained briefly with reference to FIGS. 2 and 4, as well as 3 and 5, for the resetting control can be analyzed as follows. The first solution (FIGS. 2 and 4) is largely digital with bias and scale factor internally compensated. The voltage control on the electrodes E1, E2 and linearization are matched to the stability of the pick off offset. In this situation, the requirements for relative pick off accuracy result from the potential and required bias accuracies. A range (e.g. 500 xcexcg to 10 g) results in a required bias accuracy of 5xc3x9710xe2x88x925.
Corresponding considerations with regard to the second known solution (FIGS. 3 and 5) lead to a relative pick off or bias accuracy of 1.7xc3x9710xe2x88x923 with respect to required acceleration for full-scale deflection of the pendulum of, for example, 500 xcexcg to 0.3 g. Tests verify that the control electronics for the second approach are considerably less sensitive to bias errors. However, this solution has the disadvantage that circuit complexity is considerably greater and the overall measurement range is reduced by about 25% for corresponding voltages. Furthermore, it is impossible to compensate internally for scale factor.
The theory of switched electrostatic resetting for micromechanical pendulum systems yields the following expression for mean resetting force F:
F=Q1E1((xcex94t+dt)/xcex94t)xe2x88x92Q2E2((xcex94txe2x88x92dt)/xcex94t)xe2x80x83xe2x80x83(1)
For small angles, assuming linear deflection, the normal approximation sinxcex1≈xcex1 can be assumed and the switching times for both voltages are the same. In such case:
Due to resetting forces, any asymmetry can produce an additional bias error, (referred to as the reset bias or bias B). Setting dt=0 and F=mxc2x7a (m=mass of the pendulum P, a=acceleration), bias B is obtained from (1) as:
B=(Q1E1xe2x88x92Q2E2)(1/M)xe2x80x83xe2x80x83(2)
Scale factor S for the acceleration is obtained from the component where dtxe2x89xa00:                     S        =                              (                                                            Q                  1                                ⁢                                  E                  1                                            +                                                Q                  2                                ⁢                                  E                  2                                                      )                    ⁢                      dt                          Δ              ⁢                              xe2x80x83                            ⁢              t                                ⁢                      1            m                                              (        3        )            
The range of reset acceleration for positive and negative acceleration R+ or Rxe2x88x92 is given by:                                           R            +                    =                                    [                                                                    Q                    1                                    ⁢                                                            E                      1                                        ⁡                                          (                                                                                                    Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                      dt                                                          ma                              ⁢                                                              xe2x80x83                                                            ⁢                              x                                                                                                                                Δ                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                                    )                                                                      -                                                      Q                    2                                    ⁢                                                            E                      2                                        ⁡                                          (                                                                                                    Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    -                                                      dt                                                          ma                              ⁢                                                              xe2x80x83                                                            ⁢                              x                                                                                                                                                            Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    ⁢                                                      xe2x80x83                                                                                              )                                                                                  ]                        ⁢                          1              m                                      ⁢                  
                ⁢                              R            -                    =                                    [                                                                    Q                    1                                    ⁢                                                            E                      1                                        ⁡                                          (                                                                                                    Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    -                                                      dt                                                          ma                              ⁢                                                              xe2x80x83                                                            ⁢                              x                                                                                                                                Δ                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                                    )                                                                      -                                                      Q                    2                                    ⁢                                                            E                      2                                        ⁡                                          (                                                                                                    Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                      dt                                                          ma                              ⁢                                                              xe2x80x83                                                            ⁢                              x                                                                                                                                                            Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    ⁢                                                      xe2x80x83                                                                                              )                                                                                  ]                        ⁢                          1              m                                                          (        4        )            
For simplicity, assuming that dtmax=xcex94t:                               R          +                =                                                            2                ⁢                                  Q                  1                                ⁢                                  E                  1                                            m                        ⁢                          xe2x80x83                        ⁢            and            ⁢                          xe2x80x83                        ⁢                          R              -                                =                                    2              ⁢                              Q                2                            ⁢                              E                2                                      m                                              (        5        )            
In the method described above as the first recommended solution (FIGS. 2 and 4), the voltages U1 and U2 are applied to the capacitors C1, C2:                                           Q            1                    =                                                    C                1                            ⁢                              U                1                                      =                                          ϵ                0                            ⁢                              A                                  d                  1                                            ⁢                              U                1                                                    ⁢                  
                ⁢                              Q            2                    =                                                    C                2                            ⁢                              U                2                                      =                                          ϵ                0                            ⁢                              A                                  d                  2                                            ⁢                              U                2                                                    ⁢                  
                ⁢                              E            1                    =                                    U              1                                      d              1                                      ⁢                  
                ⁢                              E            2                    =                                    U              2                                      d              2                                                          (        6        )            
In this case:
A Areas of the capacitors C1, C2; assumed equal
∈0 Dielectric constant
d1,2 Distances between the pendulum P and the respective electrodes E1 and E2.
If the following substitutions are made
d1=d0+d, d2=d0xe2x88x92d, U1=U0+U and U2=U0xe2x88x92U, where
U0=mean switching voltage, then the following formulas are obtained from equations (2), (3), (5) and equation (6) if d less than  less than d0 and U less than  less than U0:                     B        ≈                                            4              ⁢                              xe2x80x83                            ⁢              ϵ              ⁢                              xe2x80x83                            ⁢                              AU                0                2                                                    md              0              2                                ⁢                      (                                          U                                  U                  0                                            -                              d                                  d                  0                                                      )                                              (7a)                                S        ≈                                            2              ⁢                              xe2x80x83                            ⁢              ϵ              ⁢                              xe2x80x83                            ⁢                              AU                0                2                                                    md              0              2                                ⁢                      dt                          Δ              ⁢                              xe2x80x83                            ⁢              t                                                          (7b)                                R        ≈                              2            ⁢                                          ϵ                ⁢                                  xe2x80x83                                            0                        ⁢                          AU              0              2                                            md            0            2                                              (7c)            
In this approximation is R==R+=R, as is immediately evident for dt=xcex94t from equation 7b.
The major variables influencing resetting bias B, scale factor S and reset acceleration R are voltages U0 and U, and distances D0 and D. As can be seen from equation 7b, the scale factor S depends on (U0/d0)2. The first-described solution is based on the method and thus has the disadvantages, that the scale factor S depends critically on the stability of the mean switching voltage U0 and all the possible contact resistances to the electrodes, while the scale factor S similarly varies critically with changes to the mean distances D0 between the capacitors C1, C2 (due, for example, to temperature or pressure changes).
Since the resetting bias B is measured via the scale factor S as a time change dt, the dependency on (U0/d0)2 stands outxe2x80x94as can be seen from equation 7a. The resetting bias B also depends linearly on U/U0 and d/d0. The stability requirements for this increase with the reset acceleration range since it follows from equations 7a and 7c that:
B≈2R(U/U0xe2x88x92d/d0)xe2x80x83xe2x80x83(8)
The first-described solution is thus subject to the disadvantage that, for example, for a resettable acceleration range of 80 g and a resetting bias stability of 500 xcexcg, the variables that govern the relationships of the scale factor S and of the resetting bias B must be kept stable to 6xc3x9710xe2x88x926. This is particularly difficult for the variable d/d0 as, for micromechanical pendulums with realistic thickness and restricted resetting voltage, the distance D0 less than 3xc3x9710xe2x88x926 m must be complied with, resulting in accuracy requirements of d less than  less than 1.8xc3x9710xe2x88x9211 m for the deflection d.
The second solution (FIGS. 3 and 5) is based on a constant charge Q being applied to each of the two capacitors C1, C2 between the pendulum P and the electrodes E1, E2 by a constant current source 5 over a fixed predetermined time window xcex94ti. This measure is intended to result in:
Q1=Q2=Qxe2x80x83xe2x80x83(9a)
Furthermore, for the capacitors C1, C2:                     Q        =                                            ϵ              0                        ⁢                          A                              d                1                                      ⁢                          U              1                                =                                    ϵ              0                        ⁢                          A                              d                2                                      ⁢                          U              2                                                          (9a)            
It follows that:                               E          1                =                                            U              1                                      d              1                                =                                                    U                2                                            d                2                                      =                                          E                2                            =              E                                                          (        10        )            
Thus, for the resetting bias B, using equation 2:                     B        =                                            (                                                Q                  ·                  E                                -                                  Q                  ·                  E                                            )                        ⁢                          1              m                                ≡          0                                    (11a)            
For scale factor S, using equation 3:                     S        =                  2          ⁢                      Q            ·            E                    ⁢                      dt                          Δ              ⁢                              xe2x80x83                            ⁢              t                                ⁢                      1            m                                              (11b)            
The second solution is thus advantageous in that the resetting bias B disappears and the scale factor S is not dependent on the deflection d. Thus, no linearization is required. The accuracy of scale factor S corresponds to the Q-factor of the current control and the time control for current charging. If, in addition, one substitutes:
U1=U0+xcex94U
U2=U0xe2x88x92xcex94U
then equation 10 applies for all xcex94U, and thus also for xcex94U=0, from which it follows that:                     E        =                                            U              1                                      d              1                                =                                                    U                1                                            d                2                                      =                                          U                0                                            d                0                                                                        (        12        )            
This means that, for example:                                                         d              1                        -                          d              0                                            d            0                          =                                                            U                1                            -                              U                0                                                    U              0                                =                                    Δ              ⁢                              xe2x80x83                            ⁢              U                                      U              0                                                          (        13        )            
The voltage difference xcex94U thus represents a measure of the deflection of the pendulum P in response to external acceleration. This voltage difference xcex94U in the illustrated control loop influences the time difference dt of the switching pulses in such a way that the pendulum P is held at d0 with respect to the electrodes E1, E2, and acceleration is compensated. This type of charge control results in a resetting force that is independent of deflection and constant. Thus, there is no need for the otherwise-necessary linearization of the resetting force.
The latter-described method (FIGS. 2 and 4) has two considerable disadvantages,
Approximately 25% of the resetting cycle is required for application of the charges Q=ixc2x7xcex94ti, so that the maximum control time dtmax is reduced, and the range of the reset acceleration is thus restricted in accordance with equation 4.
The current i may flow only into the actual effective capacitances C1, C2 between the pendulum P and the electrodes E1, E2. However, micromechanical accelerometers generally have considerably greater stray capacitances than effective capacitances so that, in practice, this requirement results in considerable difficulties.
The preceding and other shortcomings of the prior art are addressed by the present invention that provides an improvement in an accelerometer of the type having a micromechanical pendulum, capacitive pick off and a control loop reset by electrostatic forces. The control loop, in a sequential time sequence, applies a resetting voltage between the pendulum and a first or second electrode that are fixed relative to the pendulum and aligned at respectively-defined distances from opposite surfaces of the pendulum.
The improvement to such apparatus provided by the invention includes the voltage levels of pulses that act sequentially on the two electrodes being such that no charge difference flows when the same force acts on both sides of the pendulum. Additionally, the time durations of the respectively-applied voltage pulses in response to an acceleration are responsive to the voltage differences between the two electrodes so that the difference between the time durations corresponds to the acceleration.
As a consequence, the control loop detects a charge difference flowing via the pendulum as a control variable and influences the electrostatic resetting forces on the pendulum.